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2 years ago

What is one root of this equation? 2x^-4x+9=0

Mathematics

1 answer:

Nutka1998 [239]2 years ago

3 0

9514 1404 393

Answer:

1 +i√3.5

Step-by-step explanation:

In vertex form, the equation is ...

2(x² -2x +1) +7 = 0

2(x -1)² +7 = 0

Then the solutions are ...

(x -1)² = -7/2

x = 1 ±i√3.5

One solution is 1+i√3.5.

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How to find the derivative of an integral with bounds.

Free_Kalibri [48]

Answer:

The statement of the fundamental theorem of calculus shows the upper limit of the integral as exactly the variable of differentiation. Using the chain rule in combination with the fundamental theorem of calculus we may find derivatives of integrals for which one or the other limit of integration is a function of the variable of differentiation.

Step-by-step explanation:

3 0

2 years ago

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

2 years ago

I NEED HELP AGAIN PLEASE 7 7/10+ 7 2/10

Lera25 [3.4K]

The answer is 14.9 or you can say 14 9/10.

7 0

2 years ago

Read 2 more answers

A recipe for cookies called for 2/3 of a cup of sugar per batch.Elena used 5 1/3 cups of sugar to make multiple batches of cooki

Nookie1986 [14]

Answer: 8 batches

explanation: 5 1/3 divided by 2/3 equals 8. To find out how many batches were made, you need to divide the total amount used by the amount needed for one batch.

5 0

2 years ago

Read 2 more answers

What is the value of the expression 7⋅(−5)⋅4?

Masja [62]

Multiply each number. Remember that when multiplying a negative and positive number, the outcome will be negative

7 x -5 = -35
-35 x 4 = -140

-140 is your answer

hope this helps

4 0

3 years ago

Read 2 more answers