Question 1 (1 point)

HELPPP MEE PLEASEEE I DONT WANNA FAIL SUMMER SCHOOL NO FILES OR LINKS WOULD BE DEEPLY APPRECIATED

scoray [572]

Answer:

1) 1/4

2) 1 1/2

3) 9/5

4) 4 pounds

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

A rectangle box with a square base and no top needs to be made using 300ft^2 of material. Find the dimensions of the box with th

Yuri [45]

The dimensions of the box are 10 ft and 5 ft

The maximum volume is 500 ft³

Step-by-step explanation:

A rectangle box with

A square base and no top
It needs to be made using 300 ft² of material
It has greatest volume

Surface area of a box without top (SA) = perimeter of base × height + area of the base

Volume of a box (V) = base area × height

Assume that the length of the side of the square base is x and the height of the box is y

∵ It needs to be made using 300 ft² of material

∴ The surface area of the box is 300 ft²

∵ Its base is a square of side length x ft

∴ Perimeter of the base = 4 × x = 4 x

∴ Area of the base = x²

∵ The height of the box = y ft

∵ SA = perimeter of base × height + area of the base

∵ SA = (4x)(y) + x²

∴ SA = 4xy + x²

∵ SA of the box = 300 ft²

- Equate the two expressions of SA

∴ 4xy + x² = 300

Now let us find y in terms of x

- Subtract x² from both sides

∴ 4xy = 300 - x²

- Divide each term by 4x to find y

∴ $y=\frac{75}{x}-\frac{1}{4}x$

∵ V = area of the base × height

∴ V = x² × y = x²y

- Substitute y by the equation of it above

∴ $V=x^{2}(\frac{75}{x}-\frac{1}{4}x)$

∴ $V=75x-\frac{1}{4}x^{3}$

∵ The volume of the box is greatest

- That means differentiate V and equate it by 0

∵ $\frac{dV}{dx}=75-\frac{3}{4}x^{2}$

∵ $\frac{dV}{dx}=0$ ⇒ greatest volume

∴ $75-\frac{3}{4}x^{2}=0$

- Subtract 75 from both sides

∴ $-\frac{3}{4}x^{2}=-75$

- Divide both sides by $-\frac{3}{4}$

∴ x² = 100

- Take √ for both sides

∴ x = 10

Substitute the value of x in the equation of y

∵ $y=\frac{75}{10}-\frac{1}{4}(10)$

∴ y = 5

The dimensions of the box are 10 ft and 5 ft

∵ $V=75x-\frac{1}{4}x^{3}$

∵ x = 10

∴ $V=75(10)-\frac{1}{4}(10)^{3}$

∴ $V=750-\frac{1}{4}(1000)$

∴ V = 750 - 250

∴ V = 500 ft³

The maximum volume is 500 ft³

Learn more:

You can learn more about the volume in brainly.com/question/6443737

#LearnwithBrainly

6 0

3 years ago

Need help with questions <br> 2. and 3.

emmainna [20.7K]

9514 1404 393

Answer:

2) x = 7

3) x = 5

Step-by-step explanation:

When a transversal crosses parallel lines, all of the acute angles are congruent, and all of the obtuse angles are congruent. When it crosses at right angle, all of the angles are right angles.

2) All of the angles are right angles.

11x +13 = 90

11x = 77 . . . . . . subtract 13

x = 7 . . . . . . . divide by 11

__

3) The two marked angles are acute.

16x = 80 . . . . the acute angles are congruent

x = 5 . . . . . . divide by 16

5 0

2 years ago

Julie made identical necklaces out of shell she collected at the beach all together she we use 10 Brown shells 15 black shells a

Lelu [443]

Answer:

Therefore the number of brown shells in each necklace was = 2 brown shells.

Step-by-step explanation:

If Julie made identical necklaces then we can say that number of each different colored shells were equally distributed among the necklaces.

So we can say that to find the number of necklaces we have to find the GCD (greatest common denominator) of the different colored shells.

Therefore the GCD of 10, 15 and 20 is 5.

Therefore Julia made 5 necklaces.

Therefore the number of brown shells in each necklace was = $\frac{10}{5}$ = 2 shells.

4 0

3 years ago