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2 years ago

Which of the following values is the solution to the equation

Mathematics

1 answer:

Alchen [17]2 years ago

6 0

Answer:

1.) 3

Step-by-step explanation:

Divide each side by -35. Whatever you do to one side of the equation, you must do to the other side.

$\frac{-35x}{-35}$ = $\frac{-105}{-35}$

X = 3

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Write an equation of the cosine function with amplitude pi/2 and period 3

juin [17]

Answer:

$y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)$

Step-by-step explanation:

Given

$Amplitude = \frac{\pi}{2}$

$Period = 3$

Required

Write the equivalent cosine function

The general formula is:

$y = acos(bx)$

Where

$amplitude = |a|$

$period = \frac{2\pi}{b}$

Substitute $\frac{\pi}{2}$ for amplitude in $amplitude = |a|$

$|a| = \frac{\pi}{2}$

$a = \frac{\pi}{2}$

Substitute 3 for period in $period = \frac{2\pi}{b}$

$\frac{2\pi}{b} = 3$

Multiply both sides by b

$2\pi = 3b$

Divide through by 3

$b = \frac{2\pi}{3}$

Hence;

$y = acos(bx)$ becomes

$y = \frac{\pi}{2}cos(\frac{2\pi}{3}x)$

5 0

3 years ago

Write down a simplified expression for the perimeter of this triangle:

Vinil7 [7]

Answer:

10x+11y-3w

Step-by-step explanation:

you just have to add the side up and do it by matching up with the values of the variable

8 0

3 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

nadezda [96]

Answer:

Step-by-step explanation:

We have volume of cone as

$V=\frac{1}{3} \pi r^2 h$

and for a cone always r/h = constant

Given that r' = rate of change of radius = -7 inches/sec

(Negative sign because decresing)

V' =- 948 in^3/sec

Radius = 99 inches and volume = 525 inches

Height at this instant = $\frac{525}{\frac{1}{3} \pi (99)^2} \\=\frac{0.1607}{\pi}$

Let us differentiate the volume equation with respect to t using product rule

$V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\$

$-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14 + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514$

Rate of change of height = 0.08514 in/sec

8 0

2 years ago

What is the midpoint of the line segment graphed below?

FinnZ [79.3K]

Answer:

(3.5, -4.5) or option D

Step-by-step explanation:

x) (6 + 1) / 2 = 3.5

y) (-1 + (-8)) / 2 = -4.5

3 0

3 years ago

Erica’s family is moving away from California. They decided to have a moving sale and sell each item for 70% off the price they

Burka [1]

Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.

799 x 0.70 = 559.30

549 x 0.70 = 384.30

Total: 559.30 + 384.30 = $943.60

3 0

2 years ago