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2 years ago

Can someone help please !

Mathematics

2 answers:

finlep [7]2 years ago

8 0

2

just trust me please

AysviL [449]2 years ago

5 0

Answer:

Step-by-step explanation:

$16^{\frac{1}{4} }$ can be rewritten as $\sqrt[4]{16}$ .

Solve for the 4th root of 16.

16=4*4=(2*2)(2*2)=2

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b. Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box.

Ainat [17]

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

<u>Step-by-step explanation:</u>

Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:

We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.

⇒ $2x$

The third box contained two more pounds than the first box i.e.

⇒ $x+2$

The last box contained one-fourth the amount in the second box i.e.

⇒ $(\frac{1}{4})2x = \frac{x}{4}$

Therefore , Sum of pounds of candy are :

⇒ $\frac{x}{2} +x+2+2x+x=65$

⇒ $\frac{x}{2} +4x=63$

⇒ $\frac{9x}{2}=63$

⇒ $x=63(\frac{2}{9} )$

⇒ $x=14$

Therefore , Candy in each box is :

First box = 14 pounds

Second box = 2x = 28 pounds

Third Box = x+2= 16 pounds

Fourth box = x/2 = 7 pounds

8 0

3 years ago

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

Z wants to buy five shirts worth 34 dollars each and three baseball caps worth 31

ella [17]

Answer:

$199.50

Step-by-step explanation:

10% discount of $34 = 10/100*34 = $3.40

so, a single shirt costs $34-$3.40 = $30.60

half off = 50% discount of $31 = 50/100*31 = $15.50

so, a single cap costs $31-$15.50 = $15.50

so, 5 shirts and 3 caps cost now

5*$30.60 + 3*$15.50 = $153 + $46.50 = $199.50

but careful - can this be a trick question ?

the phrasing of the problem description can also suggest that the discounts are only listed to confuse us and are already included in the mentioned prices ("worth" $34 - what does that mean ? because including the discounts they are currently "worth" their prices).

then it would just plainly be

5*$34 + 3*$31 = $170 + $93 = $263

4 0

3 years ago

I really need help and this answered ASAP. thank you and sorry.

Semenov [28]

9514 1404 393

Answer:

$2.50

Step-by-step explanation:

The question asks for the total cost of a notebook and pen together. We don't need to find their individual costs in order to answer the question.

Sometimes we get bored solving systems of equations in the usual ways. For this question, let's try this.

The first equation has one more notebook than pens. The second equation has 4 more notebooks than pens. If we subtract 4 times the first equation from the second, we should have equal numbers of notebooks and pens.

(8n +4p) -4(3n +2p) = (16.00) -4(6.50)

-4n -4p = -10.00 . . . . . . . . . . . simplify

n + p = -10.00/-4 = 2.50 . . . . divide by the coefficient of (n+p)

The total cost for one notebook and one pen is $2.50.

<em>Additional comment</em>

The first equation has 1 more notebook than 2 (n+p) combinations, telling us that a notebook costs $6.50 -2(2.50) = $1.50. Then the pen is $2.50 -1.50 = $1.00.

One could solve for the costs of a notebook (n) and a pen (p) individually, then add them together to answer the question. We judge that to be more work.

4 0

3 years ago

Read 2 more answers

Sylvia walked 34 mi east from her house to the bank. Then she walked 13 mi west to a gift shop. From the gift shop, she walke

Oduvanchick [21]

I'm thinking it is a mile from her house

5 0

3 years ago