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3 years ago

Find the distance between this pair of points (-3,5) and (5. - 1)

Mathematics

2 answers:

padilas [110]3 years ago

7 0

Answer:

14.

Step-by-step explanation:

6 down, 8 right

Misha Larkins [42]3 years ago

7 0

Answer:

10 units

Step-by-step explanation:

<u>Use distance formula:</u>

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d = \sqrt{(5 + 3)^2+(-1-5)^2} = \sqrt{8^2+6^2} =\sqrt{100} = 10$

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Evaluate the dot product of (7, 5) and (- 5, 4)

melamori03 [73]

Answer:

The dot product of (7,5) and (-5,4) is -15

Step-by-step explanation:

Given

(7,5) and (-5,4)

Required

Determine the dot product

Dot product is calculated using the following formula;

$a.b = {a_1b_1+a_2b_2+...+a_nb_n}$

Let a = (7,5) and b = (-5,4);

The above formula becomes

$a.b = {7*-5+5*4}$

$a.b = {-35+20}$

$a.b = {-15}$

Hence, the dot product of (7,5) and (-5,4) is -15

5 0

3 years ago

You are trying to forecast coffee sales for the holiday season. You sold 1,500 cups of coffee during the holidays last year, but

Airida [17]

Hello there!

You expect to sell 100% - 20% = 80% of many coffee sales.

0.80 * 1500 = 1200

Your answer is 1200 cups of coffee.

Hope I helped!

Let me know if you need anything else!

~ Zoe

5 0

3 years ago

Find -3 3/4 +1/2, i-Ready quiz

Fofino [41]

Answer: I think the answer is -3 2/5✨

4 0

2 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

Write an equation of a line in slope-intercept from with the given slope, slope:–3/4, y-intercept: –2

larisa [96]

Answer: y=-3/4x-2

Step-by-step explanation:

Write an equation of a line in slope-intercept from with the given slope, slope:–3/4, y-intercept: –2

The y-intercept is at (0,-2)

Then we write the equation using y=mx+b becuase that is the point slope form.

m=-3/4 which was given in the question

because y-intercept is at (0,-2)

y=-2

x=0

-2=-3/4(0)+b

-2=0+b

-2=b

now we know that m is -3/4 and b is -2

Hence the equation is y=-3/4x-2

7 0

3 years ago